Simon Baker
Published 2012-08-30, updated 2012-10-15Version 2
In a recent paper of Feng and Sidorov they show that for $\beta\in(1,\frac{1+\sqrt{5}}{2})$ the set of $\beta$-expansions grows exponentially for every $x\in(0,\frac{1}{\beta-1})$. In this paper we study this growth rate further. We also consider the set of $\beta$-expansions from a dimension theory perspective.
Journal: Fund. Math. 219 (2012), 271-285
On universal and periodic $β$-expansions, and the Hausdorff dimension of the set of all expansions
Badly Approximable Numbers and the Growth Rate of the Inclusion Length of an Almost Periodic Function
Sets of beta-expansions and the Hausdorff Measure of Slices through Fractals
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